Palindrome Partitioning

The problem requires finding all possible partitions of a given string s such that every substring in the partition is a palindrome. Here’s an implementation for that.

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class Solution:
    def partition(self, s: str) -> List[List[str]]:
        def is_palindrome(substring):
            return substring == substring[::-1]

        def backtrack(start, path):
            if start == len(s):
                result.append(path[:])
                return

            for end in range(start + 1, len(s) + 1):
                substring = s[start:end]
                if is_palindrome(substring):
                    path.append(substring)
                    backtrack(end, path)
                    path.pop()

        result = []
        backtrack(0, [])
        return result

Explanation

1. Define Helper Functions: Two helper functions are used - is_palindrome to check if a substring is a palindrome, and backtrack to explore different partition possibilities.

2. Backtracking: This is the primary mechanism to explore all possible partitions. It starts from the beginning of the string and recursively considers every possible substring that’s a palindrome. The function constructs paths representing valid partitions and stores them in the result.

3. Palindrome Check: Before adding a substring to the current path, we verify if it’s a palindrome using the is_palindrome function. Only palindromic substrings are considered.

Key Takeaway

The solution uses backtracking to explore all possible partitionings of the input string into palindromic substrings. By breaking the string down into smaller substrings and checking each one for palindromicity, the algorithm constructs all valid partitions, satisfying the given constraints.